Paris 13

The talks will take place in the Fermat lecture hall, in the G wing, first floor. See the map (The Galilée Institut has the number 2)

- 9h30 : Marc Lelarge Diffusions and cascades in random networks
- 10h30 : Bernard Cazelles et Anton Camacho Accounting for immunodynamics in epidemiological models
- 12h00 : Romain Guy Statistical inference for epidemic models approximated by diffusion and Gaussian processes.
- 13h00 : Lunch
- 14h15 : Pieter Trapman Long-range percolation on the hierarchical lattice
- 15h15 : Peter Windridge Law of large numbers for the SIR epidemic on a random graph with given vertex degrees

There is a google-map for the way from the Epinay-Villetaneuse station.

- Marc Lelarge : Diffusions and cascades in random networks
- Bernard Cazelles & Anton Camacho : Accounting for immunodynamics in epidemiological models Epidemiological models of influenza transmission usually assume that recovered individuals instantly develop a fully protective immunity against the infecting strain. However, recent studies have highlighted host heterogeneity in the development of this immune response, characterized by delay and even absence of protection that could lead to homologous reinfection. Here, we investigate how these immunological mechanisms at the individual level shape the epidemiological dynamics at the population level. In particular we assess their roles in driving multiple-wave influenza outbreaks. We develop a mechanistic model accounting for host heterogeneity in the immune response. Immunological parameters are inferred by confronting our dynamical model to a two-wave influenza epidemic that occurred on the remote island of Tristan da Cunha in 1971.
- Romain Guy : Statistical inference for epidemic models approximated by diffusion and Gaussian processes.
- Pieter Trapman : Long-range percolation on the hierarchical lattice
- Peter Windridge : Law of large numbers for the SIR epidemic on a random graph with given vertex degrees

The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individualsʼ behavior is the result of a strategic choice. We study a simple coordination game with binary choice and give a condition for a new action to become widespread in a random network. Our results differ strongly from the one derived with epidemic models and show that connectivity plays an ambiguous role: while it allows the diffusion to spread, when the network is highly connected, the diffusion is also limited by high-degree nodes which are very stable. In a second part (joint work with E.Coupechoux), we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We analyze the impact of clustering on the cascades (size and frequency).

Abstract

The hierarchical lattice of order N, may be seen as the leaves of an infinite regular N-tree, in which the distance between two vertices is the distance to their most recent common ancestor in the tree. We create a random graph by independent long-range percolation on the hierarchical lattice of order N: The probability that a pair of vertices at (hierarchical) distance R share an edge depends only on R and is exponentially decaying in R, furthermore the presence or absence of different edges are independent. We give criteria for percolation (the presence of an infinite cluster) and we show that in the supercritical parameter domain, the infinite component is unique. Furthermore, we show the percolation probability (the density of the infinite cluster) is continuous in the model parameters. In particular, there is no percolation at criticality. Joint work with Slavik Koval and Ronald Meester

We consider the limiting behaviour of the SIR epidemic model on a random graph chosen uniformly subject to having given vertex degrees. In the model, each vertex is either susceptible, infective or recovered. Infective vertices infect their susceptible neighbours, and recover, at a constant rate. Initially there is only one infective vertex. The infection and recovery rates, together with the limiting vertex degree distribution, determine a 'growth' parameter for the disease. If this parameter is below a (specified) critical threshold then, with high probability, only a small number of vertices ever get infected. Above the threshold there is a positive probability that many vertices get infected. In that case, the evolution of the epidemic is almost deterministic in the sense that key quantities, such as the fraction of infective vertices, are concentrated around the solutions to certain ordinary differential equations. I'll explain these results in detail and sketch our new proof. Compared to existing approaches, ours surmounts a technical assumption on the degree sequence and is shorter. This is joint work with Malwina Luczak and Svante Janson.

Last modified: 26 Oct 2012